Got this response from a TWRA official on Tndeer. Looks like they added a proclomation to let us use centerfires on WMAs that have small game seasons open with statewide
"Rifles and handguns using center-fire ammunition are legal for hunting beaver,bobcat,foxes,coyotes,wild hogs,groundhogs,and crows, ONLY DURING DEER SEASON..."
However, that paragraph was changed in the Proclamation (which is the actual regulation by law) to say:
"Rifles and handguns using center-fire ammunition are legal for hunting beaver, bobcat, foxes, coyotes, groundhogs, and crows, except during deer and bear seasons and on wild hog hunts with dogs permitted. Rifles and handguns using center-fire ammunition prohibited for hunting all small game species on wildlife management areas (except on wildlife management areas open with statewide seasons or as noted in the wildlife management area proclamation or as specified in Section 1.(2) and (5) above)"
In other words... If a Wildlife Management Area is listed as "open with statewide seasons and bag limits" for small game, coyotes may be taken with centerfire rifles. The only restriction is when it is archery only deer season, you have to use a bow to kill a coyote (otherwise people would be out there with a 30-06 claiming to be coyote hunting), and during muzzleloader/archery deer season you can only kill coyotes with a muzzleloader or a bow (for the same reason).
To reinforce the legality of shooting a coyote on a WMA in July with a .223 (as long as it is open to statewide seasons and bag limits), the following is in Proclamation 10-07:
"On WMAs open with statewide seasons, the season dates, bag limits, weapon types, and ammunition types that pertain to the county where the WMA is located apply to that WMA. Special regulations listed specifically for those WMAs still apply."
In other words, if coyote season is open on your friend's farm in the same county, it is open on the WMA.
WARNING: You need to check to make sure the WMA is open to statewide seasons and bag limits, for small game hunting, before taking a .223 to the WMA in July. If there is an exception which prevents it, you cannot. For instance, in Region I...
Barkley WMA says Big Game and Small Game are open with statewide seasons except as noted. Then it notes some exceptions (closed during late duck season in sub-impoundments, etc). Cypress Pond Refuge says Big Game and Small Game are open with statewide, except as noted, and then says, "All seasons closed during refuge closure date." That means you can hunt coyotes with a .223 in the summer, but you can't hunt them from November 15 through the last day of February, because that is the "refuge closure dates." (I know we close the refuges between Nov.15-end of Feb., but I can't find the closure dates listed anywhere in the hunting guide. The dates are listed in the Proclamation, but not in the guide. That's another mistake we need to fix.)
I know this stuff can get to be a confusing mess. If in doubt, call the manager of the specific WMA. I assure you, the intention in Region I is to allow coyote hunting just like the open county hunts, on as many WMAs as possible, and if a Region I WMA lists small game as "open with statewide seasons and bag limits," we mean it. Unless there is a SPECIFICALLY LISTED EXCEPTION. I will not speak for the other Regions.